What I have understood is that the overnight index swap is bootstrapped to discount rates/zero rates that in their turn are considered risk free. The reason being, that the reference rate of such swap - which is the overnight uncollateralized lending between banks - corresponds to overnight lending, which is close to risk-free due to its very short period.

However, what I have also understood is that settlement of these overnight swaps are usually at maturity or annually for swaps longer than 1 year. The credit risk in such swap is thus actually the same as the credit risk in any LIBOR referencing swap due to the fact that settlement/maturity occurs further in the future, allowing for more counterparty credit risk. The only difference being the reference, that is, either LIBOR or the overnight rate. It thus means that in both cases there is an additional spread on both swap rates to adjust for the swap's credit risk.

Now, one may argue that the credit risk in such swap is very small, however, the fact that we collateralize swaps, is to me, an indication that the credit risk is sufficiently significant.

Are these observations correct? If they are, how good is the approximation of the overnight index swap really to risk-free? And if they are not, please correct me.

$\begingroup$The Rate is a close approximation of the risk free rate (the rate for borrowing and lending at no risk), the Swap itself may well not be risk free (especially if it is long term) but that is a separate thing.$\endgroup$
– noob2Sep 16 '16 at 14:13

$\begingroup$Why is that a seperate thing? If the counterparty issuing the swap is very risky then I would like to be compensated for this risk and will therefore increase the swap rate, thus bringing in a component of credit risk in the OIS rate.$\endgroup$
– The BergSep 16 '16 at 14:15

$\begingroup$To give an opposite example: If Goldman and JP Morgan have a swap of Libor vs the Yield on Junk Bonds, that is a low risk Swap (for the counterparties) which references a high risk Rate.$\endgroup$
– noob2Sep 16 '16 at 14:18

$\begingroup$As you said, these are collateralized and margined. There's also virtually no counterparty risk. (The only counterparty risk is if the clearing house itself goes under.)$\endgroup$
– HelinSep 16 '16 at 14:43

$\begingroup$Keep in mind also that if OIS swap is longer than 1 year, counterparties have to make annual netting payments. Further reduces risk.$\endgroup$
– noob2Sep 16 '16 at 17:02

1 Answer
1

There's a lot of confusion here. Most Interest rate swaps (whether versus libor or another floating rate such as fed funds) have virtually no counterparty risk. That's because they are subject to daily margining, either with an exchange of directly between counterparties. The cash flows on these swaps are usually discounted at fed funds rates, because the interest paid on the margin amount is usually fed funds. It's nothing to do with the riskiness of the swap.

$\begingroup$Thanks for your answer. I think we are getting close. In your answer you make the simple deduction that "cash flows on the swaps are discounted with fed funds, because that is the interest paid on the margin amount". Could you elaborate on why that is then a sensible discounter? After a good weekend of sleep I now think the following: products that are virtually risk free should be discounted with such rate, the discounter represents the risk of the contract. As the overnight rate has virtually zero counterparty risk and an OIS is margined, we can sensibly extract a risk free curve from it.$\endgroup$
– The BergSep 19 '16 at 9:06

$\begingroup$Ok. So my statement is: All OTC derivatives whose variation margin pays interest at fed funds should be discounted at fed funds. To show this , imagine a derivative consisting of a single cashflow in the future. Let's say the PV of this flow at fed funds is K dollars. Then if the market price of the derivative is not equal to K, there is an arbitrage. That's because the variation margin allows you to borrow (or lend) the purchase price at fed funds, whereas the value of the derivative is accreting at a different rate.$\endgroup$
– dm63Sep 20 '16 at 9:56